Average Error: 11.0 → 11.0
Time: 4.0s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r827357 = x;
        double r827358 = y;
        double r827359 = z;
        double r827360 = r827358 * r827359;
        double r827361 = r827357 - r827360;
        double r827362 = t;
        double r827363 = a;
        double r827364 = r827363 * r827359;
        double r827365 = r827362 - r827364;
        double r827366 = r827361 / r827365;
        return r827366;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r827367 = x;
        double r827368 = y;
        double r827369 = z;
        double r827370 = r827368 * r827369;
        double r827371 = r827367 - r827370;
        double r827372 = t;
        double r827373 = a;
        double r827374 = r827373 * r827369;
        double r827375 = r827372 - r827374;
        double r827376 = r827371 / r827375;
        return r827376;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.0
Target1.8
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 11.0

    \[\frac{x - y \cdot z}{t - a \cdot z}\]

  2. Final simplification11.0

    \[\leadsto \frac{x - y \cdot z}{t - a \cdot z}\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))